Parallel imaging methods exploit the spatial encoding contained in independent RF coil profiles to perform image reconstruction from undersampled k-space data (1). Aliasing artifacts are removed using the spatial information of the coil profiles to fill in missing phase encode lines either in the image domain, as in SENSE (2), or in k-space, as in GRAPPA (3). Parallel imaging performance is evaluated based on the geometry factor, or g-factor, which maps the amount of noise amplification that occurs in each voxel as a result of the image reconstruction problem being underdetermined by linear dependence between the coil profiles (2,4). Extensive efforts have been invested into optimizing coil profile orthogonality for a given ROI (5) and into exploring parallel imaging with undersampled non-Cartesian k-space trajectories (6). But to date, scan acceleration has only been performed with data collected using linear gradient fields applied along X, Y, and Z. For the case of circumferentially distributed surface coils, we propose in this invention that a radially-symmetric gradient shape would be a better complement to the coil array than a linearly-varying gradient, thereby reducing the amount of data that must be acquired for imaging at a given resolution.
Gradient fields and RF coil profiles are based on fundamentally different physics and do not interfere with one another. Therefore they can be freely combined to form encoding functions that are optimized for parallel imaging (7). Linear imaging gradients create plane-wave encoding functions weighted by the coil sensitivity profile. Because these plane waves comprise the kernel of the Fourier Transform integral, linear gradients provide fast and straightforward image reconstruction via the FFT once k-space is fully populated (assuming Cartesian sampling). However, for practical applications of parallel imaging, linear gradients are not generally shaped so as to take maximum advantage of the spatial encoding inherent to surface coil profiles. Because of this, large numbers of independent coils are typically required to achieve a low g-factor at high acceleration factors (8). At exceptionally high acceleration factors such as R=6 or R=4×4, moving from 32 to 96 coils substantially lowers the g-factor, albeit at the expense of greatly increased hardware cost and complexity (9). However, at more practical reduction factors such as R=3, R=4, or even R=3×3, moving from 12 to 32 coils provides much more g-factor reduction than moving from 32 to 96 coils (9). As coil elements grow smaller and more numerous, mutual coupling is greatly compounded and the coil Q-ratio generally decreases. Also, while large arrays do offer signal-to-noise ratio improvements over volume coils, as the array size grows these gains are relegated to an ever-thinner band at periphery of the sample (10).
An alternative way to improve parallel imaging performance is by imaging at ultra-high field strengths such as 7T, where wave effects within the body dielectric cause a focusing of coil profiles, improving spatial localization and the ultimate achievable g-factor for a given acceleration factor (11). However, human imaging at 7T presently entails prohibitive costs and technical complexity arising from magnet design, B1 transmit inhomogeneity, RF specific absorption rate (SAR), and other challenges (12). Furthermore, such scanners are not yet widely available, especially in clinical settings.
Recently, non-bijective curvilinear gradients have been proposed as a way to achieve faster gradient switching and spatially-varying resolution that may be tailored to objects in the ROI. In Hennig et al (13,14), two multipolar fields are generated from the real and imaginary parts of the conformal mapping. Because this mapping preserves the local angle between the isocontours of the inputs x and y, the field shapes u and v are everywhere orthogonal (∀B1·∀B2=0) and may be used as frequency and phase encoding gradients, respectively. Since zn is analytic and satisfies Laplace's equation for all n, the shapes u and v are realizable in a physical gradient coil design. The resulting fields for a given n vary in polarity with angular location and grow as rn, where r is the distance from the center. An array of surface coils provides spatial information to resolve the remaining angular ambiguity. The reduced B0 excursion over the bore of the scanner may permit faster gradient switching times for the same dB0/dt as compared with linear gradients, potentially allowing for faster imaging without violating safety limits for peripheral nerve stimulation. However, the relatively flat frequency isocontours at the center of the FOV result in pronounced blurring in this region.